Numerical modelling of the structural behaviour of thin-walled cast magnesium components using a through-process approach

A through-process methodology for numerical simulations of the structural behaviour of thin-walled cast magnesium components is presented. The methodology consists of casting process simulations using MAGMAsoft, mapping of data from the process simulation onto a FE-mesh (shell elements) and numerical simulations using the explicit FE-code LS-DYNA. In this work, generic High Pressure Die Cast (HPDC) AM60 components have been studied using axial crushing, 3-point bending and 4-point bending tests. The experimental data are applied to obtain a validated methodology for finite element modelling of thin-walled cast components subjected to quasi-static loading. The cast magnesium alloy is modelled using a user-defined material model consisting of an elastic–plastic model based on a modified J2-flow theory and the Cockcroft–Latham fracture criterion. The fracture criterion is coupled with an element erosion algorithm available in LS-DYNA. The constitutive model and fracture criterion are calibrated both with data from material tests and data from the process simulation using MAGMAsoft.     

Estimation of forming limit diagrams by the use of the finite element method and Monte Carlo simulation

A stochastic finite element-based approach for forming limit calculations of sheets is proposed and evaluated. Material inhomogeneities are represented by spatial thickness variations of the sheet which are modelled by the use of random fields. The effects of changing the smoothness, wavelengths, amplitude and anisotropy of the field realisations on the forming limit diagram are investigated. Further, the effects of the patch size and plastic anisotropy on the forming limit diagram are studied. The assumed thickness variations result in a quite wide scatter band, and changes of the characteristics of the thickness field result in changes of the shape and variance of the forming limit diagram.     

A model for process-based crash simulation

Manufacturing of a bumper system from aluminium extrusions often involves series of forming operations performed in the soft W-temper condition, and then artificially age-hardening of the components to the material's peak hardness T6 condition. It is probable that proper finite element (FE) modelling of the crash performance of the resulting systems must rely upon a geometry obtained from an FE model following the process route, i.e., including simulation of all major forming operations. The forming operations also result in an inhomogeneous evolution of some internal variables (among others the effective plastic strain) within the shaped components. Results from tensile tests reveal that plastic straining in W-temper leads to a significant change of the T6 work-hardening curves. In addition, the tests show that the plastic pre-deformation causes a reduction of the elongation of the T6 specimens. In the present work, these process effects have been included in a user-defined elastoplastic constitutive model in LS-DYNA incorporating a state-of-the-art anisotropic yield criterion, the associated flow rule and a non-linear isotropic work hardening rule as well as some ductile fracture criteria. A first demonstration and assessment of the modelling methodology is shown by ‘through-process analysis’ of two uniaxial tensile test series. The industrial use and relevance of the modelling technique is subsequently demonstrated by a case study on an industrial bumper beam system.     

Influence of texture and grain structure on strain localisation and formability for AlMgSi alloys

The influence of texture and grain structure on strain localisation and formability is examined by experiments and numerical simulations for the extruded aluminium alloys AA6063 and AA6082. In the as-extruded condition, the AA6063 alloy has an equiaxed, recrystallised grain structure with strong cube texture, while AA6082 has a fibrous, non-recrystallised grain structure with strong β-fibre texture. By deforming and heat treating the materials after extrusion, a recrystallised equiaxed grain structure with a close to random texture is obtained for both alloys. A comprehensive test programme is conducted to determine the work hardening, plastic anisotropy and formability of the materials. Strain localisation and failure are examined by optical microscopy. An anisotropic plasticity model is calibrated for the materials and used in calculation of forming limit curves by means of the Marciniak–Kuczynski (M–K) analysis for anisotropic materials. It is found that strong cube texture leads to superior formability properties for biaxial stretching while random texture slightly lowers the formability. The strong β-fibre texture of AA6082 in the as-extruded condition leads to reduced formability. The results of the M–K analysis are very conservative compared with the experimental results, and a parametric study is undertaken to investigate the sensitivity of the predicted forming limit curves to some parameters not well defined by the experiments.     

Finite element modelling of welded aluminium members subjected to four-point bending

Finite element analyses are performed to predict the structural behaviour of welded and un-welded I-section aluminium members subjected to four-point bending. A modelling procedure using shell elements is established, where careful modelling of the inhomogeneous material properties due to welding is an important ingredient. A material model comprising anisotropic plasticity and ductile fracture is adopted. The yield function and work hardening parameters for the heat-affected zone, weld and base material are determined based on material tests and experimental data available in the literature. The numerical simulations comprise explicit analyses for a basic, relatively coarse mesh and implicit analyses for the same basic mesh and a refined mesh. Simulations are performed with perfect and imperfect geometries, since some beams fail by local buckling. The numerical results are compared with existing experimental data, and, in general, good agreement with the experimental results is obtained. However, the solutions are found to be mesh dependent for members failing by strain localisation and fracture in the tension flange.     

Determination of Ductile Fracture Parameters of a Dual‐Phase Steel by Optical Measurements

Marciniak–Kuczynski and Nakajima tests of the dual‐phase steel Docol 600DL ( www.ssab.com/ ) have been carried out for a range of stress‐states spanning from uniaxial tension to equi‐biaxial tension. The deformation histories of the specimens have been recorded by digital images, and the displacement and strain fields have been determined by post‐processing the images with digital image correlation software. The fracture characteristics of the material are presented by means of the stress triaxiality, the Lode parameter and the equivalent strain. These parameters are evaluated on the surface of the specimens based on the optical field measurements and assumptions regarding the mechanical behaviour of the material. Additionally the minor versus major principal strains up to fracture are presented. It is found that the material displays a significantly lower ductility in plane‐strain tension than in uniaxial tension and equi‐biaxial tension, and that it, in the tests exposed to local necking, undergoes large strains between the onset of necking and fracture. Fractographs of selected specimens reveal that fracture is due to growth and coalescence of voids that occur in localised areas governed by shear‐band instability.     

Behaviour of extruded aluminium alloys under proportional and non-proportional strain paths

The behaviour of the extruded aluminium alloys AA7003-T6 and AA6063-T6 under proportional and non-proportional strain paths is studied. Uniaxial tension tests in different directions are carried out for as-received profiles and profiles pre-strained in uniaxial tension. Both alloys are seen to be strongly anisotropic with respect to strength, plastic flow and elongation. The characteristic anisotropy differs between the two alloys owing to the different grain structures and textures. Two linear transformation-based anisotropic yield functions are evaluated for the alloys. It is found that the Yld2004-18p yield function proposed by Barlat et al. [Barlat, F., Aretz, H., Yoon, J.W., Karabin, M.E., Brem, J.C., Dick, R.E., 2005. Linear transformation based anisotropic yield functions. Int. J. Plasticity 21, 1009–1039] accurately represents the experimental data for both alloys. With some exceptions, pre-straining leads to an increase of the flow stress and a transient increase in the work-hardening rate. After the transient phase, the work-hardening rates are about the same for the as-received and pre-strained material. The increase of the flow stress is directional, and most significant for orthogonal sequences.     

Spatial and Temporal Characteristics of Propagating Deformation Bands in AA5182 Alloy at Room Temperature

The spatial and temporal characteristics of propagating deformation bands in the Al-Mg alloy AA5182 in O temper were studied experimentally at room temperature. Tensile tests were carried out on flat specimens at strain rates in the range from 10⁻⁵ to 10⁻¹ s⁻¹. Digital image correlation (DIC) and digital infrared thermography (DIT) were applied to monitor the propagating bands. It was found that the material exhibits a sharp yield point, and Lüders bands were seen at all the strain rates. Jerky flow took place all along the Lüders plateau. It thus seems that the Portevin–Le Chatelier (PLC) effect starts at incipient yielding and that there is no critical strain. At the end of the Lüders plateau, PLC bands immediately started to propagate back and forth along the gage section of the specimen. The work hardening of the material decreased consistently with increasing strain rate, while the flow stress on the Lüders plateau was rather unaffected by the strain rate. This indicates that the dynamic strain aging (DSA) mainly affects the strength of the interaction between mobile and forest dislocations. The strain to necking was found to decrease gradually with strain rate for this alloy, which is consistent with the lower work-hardening rate at the higher strain rates.     

Prediction of necking for two aluminum alloys under non-proportional loading by using an FE-based approach

Forming Limit Diagrams (FLDs) were found numerically for sheets under non-proportional loading by means of an FE-based Marciniak–Kuczynski (M-K) analysis. The material model used in the analysis includes two instability criteria; a non-local criterion to detect incipient localized necking and a through-thickness shear instability criterion. The objective was to study whether the effects of pre-straining on the FLD could be predicted by the chosen modeling approach, and compare the results from the two instability criteria. The results with the two criteria were different, but both criteria were able to capture the strong strain-path dependence of the FLDs as the governing phenomenon is plastic instability.